ÖMO 2012 Problem 4

In a triangle $ABC$ , let $H_a$ , $H_b$ and $H_c$ denote the base points of the altitudes on the sides $BC$ , $CA$ and $AB$ , respectively. Determine for which triangles $ABC$ two of the lengths $H_aH_b$ , $H_bH_c$ and $H_aH_c$ are equal.